Page 35 - 新思维数学活动用书9 样章

2 Expressions and formulae

Challenge

13 Arun knows this relationship between temperatures in degrees Fahrenheit (°F) and
temperatures in degrees Celsius (°C).
F = 1.8C + 32 where: F is the temperature in degrees Fahrenheit (°F)

C is the temperature in degrees Celsius (°C).

Read what Arun says.

I think a temperature
Is Arun correct? Show how you of 20 °C is higher than

worked out your answer. a temperature of 65 °F .
14 Here are two formulae that are used
in science:
−
F = ma a = vu
t
Work out the value of F when v = 32, u = 12, t = 5 and m = 30.
Explain how you worked out your answer. Show your working.
1
r
2
15 The formula for the area of a semicircle is A = π .
2
a Make r the subject of the formula.
2
b Work out the radius of a semicircle with an area of 36.2 cm . A = 36.2 cm 2
Write your answer correct to 2 significant figures (2 s.f.).
16 The diagram shows a shape made from a square and a triangle.
a Write a formula for the area (A) of the shape.
b Work out A when a = 7, b = 6 and h = 4. a

c Make a the subject of the formula. h
d Work out a when A = 174, b = 10 and h = 6. b a
17 Ria has these two cubes.
The side length of the smaller cube is x cm.

The side length of the larger cube is twice the side length of the smaller
cube.
a Write an expression for the side length of the larger cube in terms of x.
b Write a formula for the total volume (V) of the cubes in terms of x.
Write your formula in its simplest form.

c Make x the subject of your formula.
3
d The total volume of the two cubes is 576 cm .
Show that the surface area of the larger cube is 384 cm .
2
Explain how you worked out your answer.

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